The student produces evidence that demonstrates
understanding of statistics and probability concepts in the following
areas; that is, the student: 
a
Collects and organizes data to answer a question or test a hypothesis
by comparing sets of data. 
b
Displays data in line plots, graphs, tables, and charts.

c
Makes statements and draws simple conclusions
based on data; that is: 
• 
reads data in line plots, graphs, tables, and charts; 
• 
compares data in order to make true statements, e.g., “seven
plants grew at least 5 cm”; 
• 
identifies and uses the mode necessary for making true statements,
e.g., “more people chose red”; 
• 
makes true statements based on a simple concept of average (median
and mean), for a small sample size and where the situation is made
evident with concrete materials or clear representations; 
• 
interprets data to determine the reasonableness of statements about
the data, e.g., “twice as often,” “three times faster”; 
• 
uses data, including statements about the data, to make a simple
concluding statement about a situation, e.g., “This kind of
plant grows better near sunlight because the seven plants that were
near the window grew at least 5 cm.” 
d
Gathers data about an entire group or by sampling
group members to understand the concept of sample, i.e., that a large
sample leads to more reliable information, e.g., when flipping coins.

e
Predicts results, analyzes data, and finds out why some results are
more likely, less likely, or equally likely.

e
Finds all possible combinations and arrangements
within certain constraints involving a limited number of variables. 
The
student produces evidence that demonstrates understanding of statistics
and probability concepts; that is, the student: 
a
Collects data, organizes data, and displays
data with tables, charts, and graphs that are appropriate, i.e., consistent
with the nature of the data. 
b
Analyzes data with respect to characteristics
of frequency and distribution, including mode and range.

c
Analyzes appropriately central tendencies of
data by considering mean and median. 
d
Makes conclusions and recommendations based
on data analysis.

e
Critiques the conclusions and recommendations
of others’ statistics.

f
Considers the effects of missing or incorrect
information. 
g
Formulates hypotheses to answer a question
and uses data to test hypotheses.

h
Represents and determines probability as a
fraction of a set of equally likely outcomes; recognizes equally likely
outcomes, and constructs sample spaces (including those described
by numerical combinations and permutations). 
i
Makes predictions based on experimental or
theoretical probabilities.

j
Predicts the result of a series of trials once the probability for
one trial is known.

The student demonstrates understanding of
statistics and probability concepts; that is, the student: 
a
Organizes, analyzes, and displays singlevariable
data, choosing appropriate frequency distributions, circle graphs,
line plots, histograms, and summary statistics. 
b
Organizes, analyzes, and displays twovariable
data using scatter plots, estimated regression lines, and computer
generated regression lines and correlation coefficients.

c
Uses sampling techniques to draw inferences
about large populations.

d
Understands that making an inference about
a population from a sample always involves uncertainty and that the
role of statistics is to estimate the size of that uncertainty. 
e
Formulates hypotheses to answer a question
and uses data to test hypotheses. 
f
Interprets representations of data, compares
distributions of data, and critiques conclusions and the use of statistics,
both in school materials and in public documents.

g
Explores questions of experimental design,
use of control groups, and reliability. 
h
Creates and uses models of probabilistic situations
and understands the role of assumptions in this process.

i
Uses concepts such as equally likely, sample
space, outcome, and event in analyzing situations involving chance. 
j
Constructs appropriate sample spaces, and applies
the addition and multiplication principles for probabilities. 
k
Uses the concept of a probability distribution
to discuss whether an event is rare or reasonably likely.

l
Chooses an appropriate probability model and
uses it to arrive at a theoretical probability for a chance event. 
m
Uses relative frequencies based on empirical
data to arrive at an experimental probability for a chance event. 
n
Designs simulations including Monte Carlo simulations
to estimate probabilities.

o
Works with the normal distribution in some
of its basic applications.

